Chapter 4, Problem 1CR

To determine

To calculate: To write the equation of line in slope intercept form

Answer to Problem 1CR

Equation of line in slope intercept form is $y=\frac{2}{3}x+3$

Explanation of Solution

Given: Graph of line is

  

Formula Used:

Equation of line in slope intercept form is given as:

  $y=mx+c$ , where

  $\begin{array}{l}m=slope\\ c=y-intercept\end{array}$

Also, equation of line passing through two points is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the graph of line as follows:

  

From graph, line passes through the points $\left(0,3\right)$ and $\left(3,5\right)$

Thus, equation of line is calculated as follows:

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values:

  $\begin{array}{l}y-3=\frac{5-3}{3-0}\left(x-0\right)\\ y-3=\frac{2}{3}\left(x\right)\\ 3y-9=2x\\ 3y=2x+9\\ y=\frac{2}{3}x+3\end{array}$

Conclusion:

Hence, equation of line in slope intercept form is $y=\frac{2}{3}x+3$